Trotterization and Lieb-Robinson bounds
Event details
| Date | 05.07.2024 |
| Hour | 14:00 › 16:00 |
| Speaker | Perrine Vantalon |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Olivier Lévèque
Thesis advisor: Prof. Nicolas Macris
Co-examiner: Prof. Rüdiger Urbanke
Abstract
Quantum simulation aims to reproduce the dynamics of quantum systems by closely approximating the evolution of the system while minimizing the gate complexity.
State-of-the-art simulation algorithms that achieve gate complexity in $O((nt)^{1+o(1)})$ are based on the Lieb-Robinson bound and Trotterization.
We review these two techniques and consider how they can be extended to noisy systems using the Liouvillian formalism, which incorporates environmental noise into the dynamics of the system.
Background papers
- Nearly optimal lattice simulation by product formulas, Andrew M. Childs, Yuan Su, https://arxiv.org/abs/1901.00564
- Dynamical Localization in Disordered Quantum Spin Systems, Eman Hamza, Robert Sims, Günter Stolz, https://arxiv.org/abs/1108.3811
- Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems,Martin Kliesch, Christian Gogolin, Jens Eisert, https://arxiv.org/abs/1306.0716
Exam president: Prof. Olivier Lévèque
Thesis advisor: Prof. Nicolas Macris
Co-examiner: Prof. Rüdiger Urbanke
Abstract
Quantum simulation aims to reproduce the dynamics of quantum systems by closely approximating the evolution of the system while minimizing the gate complexity.
State-of-the-art simulation algorithms that achieve gate complexity in $O((nt)^{1+o(1)})$ are based on the Lieb-Robinson bound and Trotterization.
We review these two techniques and consider how they can be extended to noisy systems using the Liouvillian formalism, which incorporates environmental noise into the dynamics of the system.
Background papers
- Nearly optimal lattice simulation by product formulas, Andrew M. Childs, Yuan Su, https://arxiv.org/abs/1901.00564
- Dynamical Localization in Disordered Quantum Spin Systems, Eman Hamza, Robert Sims, Günter Stolz, https://arxiv.org/abs/1108.3811
- Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems,Martin Kliesch, Christian Gogolin, Jens Eisert, https://arxiv.org/abs/1306.0716
Practical information
- General public
- Free